TY - JOUR

T1 - Exponentiated power Lindley power series class of distributions

T2 - Theory and applications

AU - Alizadeh, M.

AU - Bagheri, S. F.

AU - Samani, E. Bahrami

AU - Ghobadi, S.

AU - Nadarajah, S.

PY - 2017

Y1 - 2017

N2 - We introduce a new four-parameter generalization of the exponentiated power Lindley (EPL) distribution, called the exponentiated power Lindley power series (EPLPS) distribution. The new distribution arises on a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the minimum lifetime value among all risks. The distribution exhibits a variety of bathtub-shaped hazard rate functions. It contains as particular cases several lifetime distributions. Various properties of the distribution are investigated including closed-form expressions for the density function, cumulative distribution function, survival function, hazard rate function, the rth raw moment, and also the moments of order statistics. Expressions for the Rényi and Shannon entropies are also given. Moreover, we discuss maximum likelihood estimation and provide formulas for the elements of the Fisher information matrix. Finally, two data applications are given showing flexibility and potentiality of the EPLPS distribution.

AB - We introduce a new four-parameter generalization of the exponentiated power Lindley (EPL) distribution, called the exponentiated power Lindley power series (EPLPS) distribution. The new distribution arises on a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the minimum lifetime value among all risks. The distribution exhibits a variety of bathtub-shaped hazard rate functions. It contains as particular cases several lifetime distributions. Various properties of the distribution are investigated including closed-form expressions for the density function, cumulative distribution function, survival function, hazard rate function, the rth raw moment, and also the moments of order statistics. Expressions for the Rényi and Shannon entropies are also given. Moreover, we discuss maximum likelihood estimation and provide formulas for the elements of the Fisher information matrix. Finally, two data applications are given showing flexibility and potentiality of the EPLPS distribution.

KW - Hazard rate function

KW - Maximum likelihood estimation

KW - Model selection criteria

KW - Power series distributions

KW - Residual life function.

UR - http://www.scopus.com/inward/record.url?scp=85027174350&partnerID=8YFLogxK

U2 - 10.1080/03610918.2017.1350270

DO - 10.1080/03610918.2017.1350270

M3 - Article

AN - SCOPUS:85027174350

SN - 0361-0918

SP - 1

EP - 33

JO - Communications in Statistics: Simulation and Computation

JF - Communications in Statistics: Simulation and Computation

ER -